Physics

Gravitation and Orbital Mechanics

522 Questions

Gravitation and orbital mechanics focus on planetary motion, elliptical orbits, and satellite deployment. Questions examine astrodynamics fundamentals, including geostationary orbits and perturbation theory. These topics are highly relevant for civil services and specialized technical examinations.

Planetary orbitsSatellite dynamicsGeostationary orbitsPerturbation theoryOrbital eccentricity

Gravitation and Orbital Mechanics Questions

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

A satellite with a mass of $M$ moves in a circular orbit of radius $R$ at a constant speed of $v$. Which of the following must be true?
(I) The net force on the satellite is equal to MR and is directed toward the centre of the orbit,
(II) The net work done on the satellite by gravity in one revolution is zero.
(III) The angular momentum of the satellite is constant.

  1. I only

  2. III only

  3. I and II only

  4. II and III only

  5. I, II and III
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

In which of the following case(s), the angular momentum is conserved ?

  1. The planet Neptune moves in elliptical orbit around the sun with sun at one focus

  2. A solid sphere rolling on an inclined plane

  3. An electron revolving around the nucleus in an elliptical orbit
  4. An $\alpha $ particle approaching a heavy nucleus from sufficient distance.
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
Explanation

Angular momentum is conserved if net external torque is zero
(A) torque about sun is zero , $\because$ line of focus passer though it and no external force is present.
(B) Torque of friction is present 
(C) Force on the electron is internal , $\therefore$ torque is zero 
(D) No external force is present which may produce changes in angular momentum.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Which one of the following statements is correct?

  1. The energy required to rocket an orbiting satellite out of earth's gravitational influence is more than the energy required to project a stationary object at the same height (as the satellite) out of earth's influence.

  2. If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of potential energy.

  3. The first artificial satellite Sputnik I was launched in the year 1950.
  4. The orbital speed of the SYNCOMS (synchronous communications satellite) is $3.07\times10^{2}m s^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The energy required to rocket an orbiting satellite out of earth's gravitational influence is less than the energy required to project a stationary object at the same height (as the satellite) out of earth's influence.
Hence, option (a) is incorrect statement.


If zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic energy.
Hence, option (b) is an incorrect statement.

The first artificial satellite was launched by Soviet scientists in the year 1957.
Hence, option (c) is an incorrect statement.

The orbital speed of the SYNCOMS is $v=\dfrac{2\pi{r}}{T}=\dfrac{2\times3.14\times4.22\times10^{7}}{8.64\times10^{5}}$
$=3.07\times10^{2}m s^{-1}$
Hence, option (d) is a correct statement.

Multiple choice evs search of life outside earth types of artificial satellites geostationary orbits moon and stars in sky

Out of the following, the only correct statement about satellites is

  1. A satellite cannot move in a stable orbit in a plane passing through the earth's centre

  2. Geostationary satellites are launched in the equatorial plane

  3. Satellites are rectangular in shape.

  4. Geostationary satellites are launched in axial plane
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Geostationary satellites are launched to the equitorial plane, so the it could have a time period of 24 hours exact and can have maximum reach, i.e on both heminpheres for information transfer.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

A satellite is orbiting around the earth in an orbit in equatorial plane, of radius 2$R _{e}$ , where $R _{e}$ is theradius of the earth. Find the area on the earth, this satellite covers for communication purpose in its complete revolution 

  1. $4\pi R _{e}^{2}$
  2. $2\pi\sqrt{3} R _{e}^{2}$
  3. $2\pi(2-\sqrt{3}) R _{e}^{2}$
  4. $2\pi(4+\sqrt{3}) R _{e}^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Two satellites A & B go around the earth in a circular orbits at a heigh of $R _{A} & R _{B}$ respectively from surface of the earth. Assume earth to be a uniform sphere of radius $R _{e}$ The ratio of the magnitudes of velocities of the satellite $V _{A}/V _{B}$ is

  1. $\sqrt{\frac{R _{A}}{R _{B}}}$
  2. $\left ( R _{A}/R _{B} \right )^{2}$
  3. $\frac{R _{B}+R _{e}}{R _{A}+R _{e}}$
  4. $\sqrt{\frac{R _{B}+R _{e}}{R _{A}+R _{e}}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

To have an earth synchronous satellites it should be launched at the proper height moving from

  1. North to South in a polar plane

  2. East to West in an equatorial plane

  3. South to North in a polar plane

  4. West to East in an equatorial plane
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sense of synchronous satellite must be same as the sense of rotation of earth i.e., from west to east

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

The time period of geostationary satellite is :

  1. Zero
  2. $24 h$
  3. $12 h$
  4. $48 h$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Answer is B.

A geostationary orbit can only be achieved at an altitude very close to $35,786$ km $(22,236 mi)$, and directly above the Equator. This equates to an orbital velocity of $3.07 km/s (1.91 mi/s)$ or an orbital period of $1,436$ minutes, which equates to almost exactly one sidereal day or $23.934461223$ hours, which is approximately $24$ hours.